n^2+n=10000

Solution for n^2+n=10000 equation:

Simplifying
n2 + n = 10000

Reorder the terms:
n + n2 = 10000

Solving
n + n2 = 10000

Solving for variable 'n'.

Reorder the terms:
-10000 + n + n2 = 10000 + -10000

Combine like terms: 10000 + -10000 = 0
-10000 + n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10000' to each side of the equation.
-10000 + n + 10000 + n2 = 0 + 10000

Reorder the terms:
-10000 + 10000 + n + n2 = 0 + 10000

Combine like terms: -10000 + 10000 = 0
0 + n + n2 = 0 + 10000
n + n2 = 0 + 10000

Combine like terms: 0 + 10000 = 10000
n + n2 = 10000

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
n + 0.25 + n2 = 10000 + 0.25

Reorder the terms:
0.25 + n + n2 = 10000 + 0.25

Combine like terms: 10000 + 0.25 = 10000.25
0.25 + n + n2 = 10000.25

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 10000.25

Calculate the square root of the right side: 100.001249992

Break this problem into two subproblems by setting 
(n + 0.5) equal to 100.001249992 and -100.001249992.

Subproblem 1
n + 0.5 = 100.001249992

Simplifying
n + 0.5 = 100.001249992

Reorder the terms:
0.5 + n = 100.001249992

Solving
0.5 + n = 100.001249992

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = 100.001249992 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = 100.001249992 + -0.5
n = 100.001249992 + -0.5

Combine like terms: 100.001249992 + -0.5 = 99.501249992
n = 99.501249992

Simplifying
n = 99.501249992

Subproblem 2
n + 0.5 = -100.001249992

Simplifying
n + 0.5 = -100.001249992

Reorder the terms:
0.5 + n = -100.001249992

Solving
0.5 + n = -100.001249992

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-0.5' to each side of the equation.
0.5 + -0.5 + n = -100.001249992 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + n = -100.001249992 + -0.5
n = -100.001249992 + -0.5

Combine like terms: -100.001249992 + -0.5 = -100.501249992
n = -100.501249992

Simplifying
n = -100.501249992

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {99.501249992, -100.501249992}